Laminar buoyant magnetohydrodynamic flow in vertical rectangular ducts

Abstract

The buoyancy-driven laminar magnetohydrodynamic flow in long vertical channels is investigated. It is assumed that the channels have a rectangular cross section with one pair of walls aligned with the strong uniform magnetic field. The walls may have arbitrary electrical conductance. Using asymptotic methods, solutions are derived for general temperature distributions inside the ducts. Results are shown for different values of the control parameters. One finds the typical subregions for the flow inside the duct, namely the inviscid core, surrounded by viscous Hartmann layers and side layers. The character of the solution inside these regions may deviate from what is expected by a comparison with the classical solutions for pressure-driven duct flows. The main difference is that the flow in the core not necessarily exhibits a two-dimensional behavior. Most surprising, however, is the fact, that high-velocity jets are observed for the first time along perfectly conducting sidewalls. These jets are able to carry a major part of the flow rate.